Extrapolation for Higher Orders of Convergence

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Abstract
A new extrapolation procedure which encompasses Aitken's δ2 process and extends to higher orders of convergence is presented. The new extrapolation yields information as to whether an algorithm is converging or diverging as well as a new approximation to the solution point. The new extrapolation technique is compared with existing higher order extrapolation techniques. The value of the new extrapolation is demonstrated analytically and empirically.

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